Physical observables to determine the nature of membrane-less cellular sub-compartments
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Evaluation Summary:
There has been a lively debate recently concerning the multiplicity of reported observations of phase-separated compartments inside of cells. Specifically, some claims of phase separation have been challenged, and an alternative model put forward in which clustering of observed particles is due to a clustering of binding sites with no phase separation. The current study does an admirable job of proposing and analyzing ways of distinguishing these two scenarios.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)
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Abstract
The spatial organization of complex biochemical reactions is essential for the regulation of cellular processes. Membrane-less structures called foci containing high concentrations of specific proteins have been reported in a variety of contexts, but the mechanism of their formation is not fully understood. Several competing mechanisms exist that are difficult to distinguish empirically, including liquid-liquid phase separation, and the trapping of molecules by multiple binding sites. Here, we propose a theoretical framework and outline observables to differentiate between these scenarios from single molecule tracking experiments. In the binding site model, we derive relations between the distribution of proteins, their diffusion properties, and their radial displacement. We predict that protein search times can be reduced for targets inside a liquid droplet, but not in an aggregate of slowly moving binding sites. We use our results to reject the multiple binding site model for Rad52 foci, and find a picture consistent with a liquid-liquid phase separation. These results are applicable to future experiments and suggest different biological roles for liquid droplet and binding site foci.
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Author Response:
Reviewer #1 (Public Review):
The authors propose several ways of leveraging single-particle tracking experiments to distinguish between intracellular phase separation and an alternative model of clustered binding sites. The first proposed scheme is particularly intuitively appealing: in the binding site scenario, the local density of binding sites both increases particle density and slows effective particle diffusion, leading to a definite relationship between these two quantities, while the phase separation scenario would not necessarily couple these two quantities. The additional schemes based on particle movement near a cluster boundary, angles between consecutive steps, and search times add to the arsenal of potential analysis tools. Overall, the work is timely, rigorous, and generally clearly presented and given …
Author Response:
Reviewer #1 (Public Review):
The authors propose several ways of leveraging single-particle tracking experiments to distinguish between intracellular phase separation and an alternative model of clustered binding sites. The first proposed scheme is particularly intuitively appealing: in the binding site scenario, the local density of binding sites both increases particle density and slows effective particle diffusion, leading to a definite relationship between these two quantities, while the phase separation scenario would not necessarily couple these two quantities. The additional schemes based on particle movement near a cluster boundary, angles between consecutive steps, and search times add to the arsenal of potential analysis tools. Overall, the work is timely, rigorous, and generally clearly presented and given the growing list of reported observations of phase separation, will appeal to a broad audience.
We thank the referee for the positive attitude towards our work and are happy for the insightful comments that have increased the value of this paper.
Reviewer #3 (Public Review):
Membraneless condensates have recently become a central focus of the molecular and cellular biophysics communities. While the dominant paradigm for their formation, liquid-liquid phase separation (LLPS), has been well established in a number of cases for large, optically resolved droplets, there are significant concerns regarding the generality of this mechanism for smaller foci or puncta, and other mechanisms have been proposed to explain their formation. The problem is that it is very difficult to distinguish experimentally between these mechanisms for sub-optical resolution condensates. In this article, Heltberg et al propose a novel method, based on the analysis of single molecule tracks, that allows discriminating between the liquid phase model (LPM) and one of the challenger mechanisms, the "polymer bridging model" (PBM). This method relies on the statistics of individual displacements - diffusion, radial displacements, angular changes - which are showed theoretically to exhibit different signatures for the two models. With realistic data this is sufficient to discriminate between the models: for instance in the case of double strand break foci (DSB), building on a recent work by some of the same authors, this article convincingly rules out the PBM in favor of the LPM. The author also investigate the influence on these two models on the search time to reach a specific small target - a commonly invoked role of condensates - and show that only the LPM substantially accelerates this, which could provide additional means to experimentally discriminate between the mechanisms, on top of the intrinsic interest of this finding.
This article is a welcome addition to the literature in this field, as it will help clarify the nature of these condensates, in particular below the optical resolution. It is well-written, interesting and the conclusions are justified. I particularly appreciate the effort to employ simulated data that are realistic for actual experiments, which strengthens the claims of applicability. Some aspects of the data analysis and of the modeling, however, are insufficiently discussed and would need to be precised / expanded.
- The modeling is made under the assumption of thermal equilibrium, without further discussion. The authors should comment on why this is reasonable, in particular in view of the presence of active fluctuations and of chemical reactions in these condensates.
First of all, the experimental measurements are carried out after the formation of the foci, and the time of observation (tens of seconds) is small compared the the lifetime of foci (tens of minutes). Therefore we can assume that these measurements are not affected by the effects of formation and disruption of foci. Secondly, the data extracted to compute the results of Figure 2 (in particular for Figure 2H) are not very sensitive to the active fluctuations, since we derive an average diffusion coefficient inside and outside of the focus as well as a free energy difference between an inside and outside level. It is indeed very likely that the soup of proteins that forms the focus is active, however Rad52 is not involved in chemical reactions at the timescales we are looking at may be considered passive. This is supported by our investigations of the experimental results, where we have not seen any statistical differences as a function of the time of measurements, and we have no reason to believe that active fluctuations affect the diffusivity of Rad52 on the observed timescales. Regarding binding sites, they may also diffuse actively along with the genome and chromatin, but we describe this by an effective description of the motion of Rad52 on short time scales, so that active effects are folded into an effective diffusivity (left as a free parameter).
We want to highlight this issue as well as present our arguments of why this description is valid for the experiments considered in this work. We have added text between Eq. 6 and Eq. 7 summarizing the arguments outlined above.
- How is the diffusivity measured? Are these measures corrected for experimental error (e.g. using three-point estimators)?
Estimates of the diffusion coefficients in Min´e-Hattab et al. 2021 were obtained in different ways. Our main method is to generate the displacement histogram, and then estimate the number of different diffusion coefficients in the population based on likelihood fitting and KStesting. Then we take for all the traces, and find the ones that we are certain belong to the slowest diffusion coefficient. These traces are the ones in the focus, but by doing it this way, we are not vulnerable to the position of the boundary and to determine which are in the focus based on their position. Then we compute the MSD curves for this distribution of slowly diffusing molecules, and fit the diffusion coefficient based on a confined fit (which has a good p-value). This method is strong since we are fitting a slow diffusion population and typically can reject traces belonging to the fast diffusion coefficient. We also include the possibility of separating traces if the molecule goes from inside the focus to outside or the other way round. The alternative way we calculated the diffusion coefficient, was based on the microscopy data, where we “cropped” all the traces that could be visibly identified as being inside the focus. This method had the strength that we could visibly follow all traces, but the drawback that we could mistakenly identify molecules as being inside the focus, then they could be under or above the focus, as discussed in the section above. However both method yielded similar results. It is also based on these methods that we extract the size of the focus.
In order to clarify this important point, we have added two sentences in the caption to Table I, describing how the diffusion was measured in the experimental paper, and added a new paragraph about experimental measurements in Materials and Methods. In addition, we have clarified in the caption of Fig. 2F that we extract the maximum likelihood value of D˜(r) in each radial segment.
- The conditioning of the averages should be discussed, e.g. in Eq. 13: I assume that it is in the Ito convention? Similarly for the angle changes.
We assume that the density of the binding sites, follow a radial distribution, with no significant angular dependency. Thus the average displacement hdri is computed as a function of the initial position of the particle and averaged over all initial displacements with similar radial positions. It is indeed formulated in the Ito convention, which is why the “spurious” term appear in the first term of the second line of equation 13.
To clarify that we are using Ito convention, we have stated that we are using Ito convention for this paper, just before the introduction of eq. 1. We have furthermore clarified in the section related to eq. 13 and the section related to the distribution of the angles that we use the initial position when calculating the difference between the two connected points.
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Evaluation Summary:
There has been a lively debate recently concerning the multiplicity of reported observations of phase-separated compartments inside of cells. Specifically, some claims of phase separation have been challenged, and an alternative model put forward in which clustering of observed particles is due to a clustering of binding sites with no phase separation. The current study does an admirable job of proposing and analyzing ways of distinguishing these two scenarios.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
The authors propose several ways of leveraging single-particle tracking experiments to distinguish between intracellular phase separation and an alternative model of clustered binding sites. The first proposed scheme is particularly intuitively appealing: in the binding site scenario, the local density of binding sites both increases particle density and slows effective particle diffusion, leading to a definite relationship between these two quantities, while the phase separation scenario would not necessarily couple these two quantities. The additional schemes based on particle movement near a cluster boundary, angles between consecutive steps, and search times add to the arsenal of potential analysis tools. Overall, the work is timely, rigorous, and generally clearly presented and given the growing list of …
Reviewer #1 (Public Review):
The authors propose several ways of leveraging single-particle tracking experiments to distinguish between intracellular phase separation and an alternative model of clustered binding sites. The first proposed scheme is particularly intuitively appealing: in the binding site scenario, the local density of binding sites both increases particle density and slows effective particle diffusion, leading to a definite relationship between these two quantities, while the phase separation scenario would not necessarily couple these two quantities. The additional schemes based on particle movement near a cluster boundary, angles between consecutive steps, and search times add to the arsenal of potential analysis tools. Overall, the work is timely, rigorous, and generally clearly presented and given the growing list of reported observations of phase separation, will appeal to a broad audience.
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Reviewer #2 (Public Review):
Heltberg et al. investigate two possible mechanisms for the formation of nuclear foci and how these mechanisms can be distinguished experimentally, based on single-particle tracking of molecules that are up-concentrated in the focus. First, liquid-liquid phase separation (here: Liquid Phase Model, LPM) is treated as one of the major mechanisms currently hypothesized. Second, as an alternative mechanism, a polymer-bridging model (PBM) is investigated, in which the focus is held together by polymer bridges and contains binding sites, which can lead to local enrichment, appearing as a focus.
The theory is presented in a clean way, and while the Langevin equation for single molecules in a phase-separated liquid comes without derivation, it is plausible, and in fact backed up by our own calculations. A similar …
Reviewer #2 (Public Review):
Heltberg et al. investigate two possible mechanisms for the formation of nuclear foci and how these mechanisms can be distinguished experimentally, based on single-particle tracking of molecules that are up-concentrated in the focus. First, liquid-liquid phase separation (here: Liquid Phase Model, LPM) is treated as one of the major mechanisms currently hypothesized. Second, as an alternative mechanism, a polymer-bridging model (PBM) is investigated, in which the focus is held together by polymer bridges and contains binding sites, which can lead to local enrichment, appearing as a focus.
The theory is presented in a clean way, and while the Langevin equation for single molecules in a phase-separated liquid comes without derivation, it is plausible, and in fact backed up by our own calculations. A similar Langevin equation is found for the PBM and it is subsequently shown that both models can lead to very similar displacement distributions, thus showing that this simple observable cannot always distinguish between PBM and LPM.
Subsequently, the authors derive an effective description of the PBM, based on the experimental observation that potential binding sites on the DNA (proxied by Rfa1, a DNA-binding protein) diffuse much more slowly than a typical repair factor (represented by Rad52). Thus there is a separation of time scales between the two relevant diffusion processes, which is used to constrain the possible parameter combinations for the PBM. Based on these constraints, the authors shown that PBM is incompatible with their previous experimental results.
The remainder of the paper deals with a number of interesting observables, such as the angular distribution of displacements and search time to find a repair target, which can also be used to distinguish PBM and LPM with an ideal setup.
Strengths:
Heltberg et al. present a clean way to distinguish LPM on the one hand, and a realization of PBM on the other hand, based on theory. This is validated by comparison to data they obtained in previous work. The theory is rigorous and the data analysis is well carried out, save for minor ambiguities, which can likely be eliminated during revision. The paper draws its main strength from its interdisciplinarity.
(Minor) Weaknesses:
While the PBM presented here seems like a reasonable model if one were to think of alternatives to LPM, it is always possible to think of more specialized models with additional parameters and mechanisms to account for the same observations. In interpreting this study and its conclusions it is thus important to keep in mind that the PBM presented here is not the only possible realization of a model that can give rise to focus formation. It would be interesting to explore alternatives that are less dependent on the precise form of the potential chosen here and which might treat the polymer bridges more directly. Also, thinking of possible multi-species extensions might be an interesting future direction.
It would be helpful to back up the rates which were not measured experimentally by suitable references or discuss more transparently where assumptions were made that have not been investigated in the literature.
Conclusions and Discussion:
The authors have achieved their goal of distinguishing LPM and PBM. The corresponding theory will be of great use for everyone in the field aiming to make this distinction based on single molecule tracking, a strategy that has been attempted numerous times, but eventually always failed due to the lack of an appropriate theoretical framework. Heltberg et al. have gone on to show a striking difference between experimentally constrained PBM realizations and the experimental measurements themselves, rendering the PBM much less likely than the LPM.
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Reviewer #3 (Public Review):
Membraneless condensates have recently become a central focus of the molecular and cellular biophysics communities. While the dominant paradigm for their formation, liquid-liquid phase separation (LLPS), has been well established in a number of cases for large, optically resolved droplets, there are significant concerns regarding the generality of this mechanism for smaller foci or puncta, and other mechanisms have been proposed to explain their formation. The problem is that it is very difficult to distinguish experimentally between these mechanisms for sub-optical resolution condensates. In this article, Heltberg et al propose a novel method, based on the analysis of single molecule tracks, that allows discriminating between the liquid phase model (LPM) and one of the challenger mechanisms, the "polymer …
Reviewer #3 (Public Review):
Membraneless condensates have recently become a central focus of the molecular and cellular biophysics communities. While the dominant paradigm for their formation, liquid-liquid phase separation (LLPS), has been well established in a number of cases for large, optically resolved droplets, there are significant concerns regarding the generality of this mechanism for smaller foci or puncta, and other mechanisms have been proposed to explain their formation. The problem is that it is very difficult to distinguish experimentally between these mechanisms for sub-optical resolution condensates. In this article, Heltberg et al propose a novel method, based on the analysis of single molecule tracks, that allows discriminating between the liquid phase model (LPM) and one of the challenger mechanisms, the "polymer bridging model" (PBM). This method relies on the statistics of individual displacements - diffusion, radial displacements, angular changes - which are showed theoretically to exhibit different signatures for the two models. With realistic data this is sufficient to discriminate between the models: for instance in the case of double strand break foci (DSB), building on a recent work by some of the same authors, this article convincingly rules out the PBM in favor of the LPM. The author also investigate the influence on these two models on the search time to reach a specific small target - a commonly invoked role of condensates - and show that only the LPM substantially accelerates this, which could provide additional means to experimentally discriminate between the mechanisms, on top of the intrinsic interest of this finding.
This article is a welcome addition to the literature in this field, as it will help clarify the nature of these condensates, in particular below the optical resolution. It is well-written, interesting and the conclusions are justified. I particularly appreciate the effort to employ simulated data that are realistic for actual experiments, which strengthens the claims of applicability. Some aspects of the data analysis and of the modeling, however, are insufficiently discussed and would need to be precised / expanded.
The modeling is made under the assumption of thermal equilibrium, without further discussion. The authors should comment on why this is reasonable, in particular in view of the presence of active fluctuations and of chemical reactions in these condensates.
How is the diffusivity measured? Are these measures corrected for experimental error (e.g. using three-point estimators)?
The conditioning of the averages should be discussed, e.g. in Eq. 13: I assume that it is in the Ito convention? Similarly for the angle changes.
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